Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

The cluster value problem in spaces of continuous functions


Authors: W. B. Johnson and S. Ortega Castillo
Journal: Proc. Amer. Math. Soc. 143 (2015), 1559-1568
MSC (2010): Primary 32-XX; Secondary 46-XX
DOI: https://doi.org/10.1090/S0002-9939-2014-12190-3
Published electronically: December 10, 2014
MathSciNet review: 3314069
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We study the cluster value problem for certain Banach algebras of holomorphic functions defined on the unit ball of a complex Banach space $ X$. The main results are for spaces of the form $ X=C(K).$


References [Enhancements On Off] (What's this?)

  • [1] Fernando Albiac and Nigel J. Kalton, Topics in Banach space theory, Graduate Texts in Mathematics, vol. 233, Springer, New York, 2006. MR 2192298 (2006h:46005)
  • [2] R. M. Aron, P. D. Berner, A Hahn-Banach extension theorem for analytic mappings, Bull. Soc. math. France 106 (1978), pp. 3-24.
  • [3] R. M. Aron, B. J. Cole, T. W. Gamelin, Spectra of algebras of analytic functions on a Banach space, J. reine angew. Math 415 (1991), pp. 51-93.
  • [4] Richard M. Aron, Daniel Carando, T. W. Gamelin, Silvia Lassalle, and Manuel Maestre, Cluster values of analytic functions on a Banach space, Math. Ann. 353 (2012), no. 2, 293-303. MR 2915537, https://doi.org/10.1007/s00208-011-0681-0
  • [5] Robert Braun, Wilhelm Kaup, and Harald Upmeier, On the automorphisms of circular and Reinhardt domains in complex Banach spaces, Manuscripta Math. 25 (1978), no. 2, 97-133. MR 500878 (80g:32003), https://doi.org/10.1007/BF01168604
  • [6] C. Bessaga and A. Pełczyński, Spaces of continuous functions. IV. On isomorphical classification of spaces of continuous functions, Studia Math. 19 (1960), 53-62. MR 0113132 (22 #3971)
  • [7] B. J. Cole, T. W. Gamelin, W. B. Johnson, Analytic Disks in Fibers over the Unit Ball of a Banach Space, Michigan Math. J. 39 (1992), pp. 551-569.
  • [8] Seán Dineen, Complex analysis on infinite-dimensional spaces, Springer Monographs in Mathematics, Springer-Verlag London Ltd., London, 1999. MR 1705327 (2001a:46043)
  • [9] J. Duncan and S. A. R. Hosseiniun, The second dual of a Banach algebra, Proc. Roy. Soc. Edinburgh Sect. A 84 (1979), no. 3-4, 309-325. MR 559675 (81f:46057), https://doi.org/10.1017/S0308210500017170
  • [10] Theodore W. Gamelin, Analytic functions on Banach spaces, Complex potential theory (Montreal, PQ, 1993) NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., vol. 439, Kluwer Acad. Publ., Dordrecht, 1994, pp. 187-233. MR 1332962 (96m:46082)
  • [11] Jorge Mujica, Complex analysis in Banach spaces, Holomorphic functions and domains of holomorphy in finite and infinite dimensions, North-Holland Mathematics Studies, vol. 120, North-Holland Publishing Co., Amsterdam, 1986. Notas de Matemática [Mathematical Notes], 107. MR 842435 (88d:46084)
  • [12] A. Pełczyński and Z. Semadeni, Spaces of continuous functions. III. Spaces $ C(\Omega )$ for $ \Omega $ without perfect subsets, Studia Math. 18 (1959), 211-222. MR 0107806 (21 #6528)
  • [13] Shôichirô Sakai, $ C^*$-algebras and $ W^*$-algebras, Springer-Verlag, New York, 1971. Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 60. MR 0442701 (56 #1082)
  • [14] Jean-Pierre Vigué, Le groupe des automorphismes analytiques d'un domaine borné d'un espace de Banach complexe. Application aux domaines bornés symétriques, Ann. Sci. École Norm. Sup. (4) 9 (1976), no. 2, 203-281. MR 0430335 (55 #3340)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 32-XX, 46-XX

Retrieve articles in all journals with MSC (2010): 32-XX, 46-XX


Additional Information

W. B. Johnson
Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843
Email: johnson@math.tamu.edu

S. Ortega Castillo
Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843
Email: ortega@math.tamu.edu

DOI: https://doi.org/10.1090/S0002-9939-2014-12190-3
Received by editor(s): November 3, 2012
Received by editor(s) in revised form: December 22, 2012, February 25, 2013, and July 8, 2013
Published electronically: December 10, 2014
Additional Notes: The authors were supported in part by NSF DMS 10-01321
Communicated by: Thomas Schlumprecht
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society